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51.
We present a series of studies to solve the spin-weighted spheroidal wave equation by using the method of super-symmetric quantum mechanics. We first obtain the first four terms of super-potential of the spin-weighted spheroidal wave equation in the case of s = 1. These results may help summarize the general form for the n-th term of the super-potential, which is proved to be correct by means of induction. Then we compute the eigen-values and the eigen- functions for the ground state. Finally, the shape-invariance property is proved and the eigen-values and eigen-functions for excited states are obtained. All the results may be of significance for studying the electromagnetic radiation processes near rotating black holes and computing the radiation reaction in curved space-time. 相似文献
52.
53.
本文在处理InAs单电子量子点哈密顿模型时,将自旋-轨道(SO)相互作用作为微扰项,计算在Fock-Darwin本征函数下SO相互作用的矩阵元,利用其对能级和波函数的二阶修正,并且考虑新的能级对g因子和有效质量m*的影响,计算得到在声子协助下电子的自旋弛豫率Γ的表达式.给出了InAs量子点中声子协助的电子自旋弛豫率Γ对于限制势频率ω0、温度T、纵向高度z0关键词:
自旋弛豫率
自旋-轨道(SO)相互作用
InAs量子点
Fock-Darwin本征函数 相似文献
54.
Peng‐Dong Fan 《International journal of quantum chemistry》2001,83(5):259-270
Using the right‐induced technique and the eigenfunction method, concise algebraic expressions of the projection operators for both single‐valued and double‐valued representations are found for the group chain O?T?C3 in terms of the projection operators of T?C3. Extremely simple relations are discovered between the symmetry adapted functions (SAFs) of the groups T and O; namely the SAFs of the subgroup T which have proper symmetry are the SAFs of the group O. The projection operators and SAFs are functions of only the quantum numbers of the group chain [the analogy of ( j,m) for the group chain SO3?SO2], without involving any irreducible matrix elements. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 259–270, 2001 相似文献
55.
In this work, we study the existence of eigenvalues for a type of non-linear equations and we give some conditions to get positive eigenfunctions. Particularly, we show that under some appropriate conditions, the set of eigenvalues is an interval. 相似文献
56.
一类两边界条件含参数的Sturm-Liouville问题 总被引:1,自引:0,他引:1
考虑第一个边界条件为参数的线性函数,第二个边界条件为有理函数的Sturm-Liouville问题.给出问题的特征值、特征函数的渐近式以及特征函数的振荡理论,并给出相应的应用实例. 相似文献
57.
O. V. Matusevich V. A. Trofimov 《Computational Mathematics and Mathematical Physics》2008,48(4):677-687
An iterative method is proposed to determine the eigenfunctions of a system of two nonlinear Schrödinger equations governing the interaction of two femtosecond pulses in a medium with quadratic and cubic nonlinearity. The method produces soliton solutions of a new form for a wide range of nonlinearity coefficients corresponding to the first and second eigenvalues. A specially chosen initial approximation is required to determine the third and higher eigenfunctions. 相似文献
58.
We use the functional principal component analysis (FPCA) to model and predict the weight growth in children. In particular,
we examine how the approach can help discern growth patterns of underweight children relative to their normal counterparts,
and whether a commonly used transformation to normality plays any constructive roles in a predictive model based on the FPCA.
Our work supplements the conditional growth charts developed by Wei and He (2006) by constructing a predictive growth model
based on a small number of principal components scores on individual’s past.
This work was supported by National Natural Science Foundation of China (Grant No. 10828102), a Changjiang Visiting Professorship,
the Training Fund of Northeast Normal University’s Scientific Innovation Project (Grant No. NENU-STC07002) and the National
Institutes of Health Grant of USA (Grant No. R01GM080503-01A1). 相似文献
59.
We propose a method for the computation of eigenvalues with odd multiplicities for spectral boundary-value problems of the 4th order with separated boundary conditions. In this method approximate eigenvalues appear as zeros of a certain function f(λ) which admits an explicit representation. 相似文献
60.
Discontinuous Sturm-Liouville Problems Containing Eigenparameter in the Boundary Conditions 总被引:3,自引:0,他引:3
M. KADAKAL O. Sh. MUKHTAROV 《数学学报(英文版)》2006,22(5):1519-1528
In this paper, discontinuous Sturm-Liouville problems, which contain eigenvalue parameters both in the equation and in one of the boundary conditions, are investigated. By using an operatortheoretic interpretation we extend some classic results for regular Sturm-Liouville problems and obtain asymptotic approximate formulae for eigenvalues and normalized eigenfunctions. We modify some techniques of [Fulton, C. T., Proc. Roy. Soc. Edin. 77 (A), 293-308 (1977)], [Walter, J., Math. Z., 133, 301-312 (1973)] and [Titchmarsh, E. C., Eigenfunctions Expansion Associated with Second Order Differential Equations I, 2nd edn., Oxford Univ. Pres, London, 1962], then by using these techniques we obtain asymptotic formulae for eigenelement norms and normalized eigenfunctions. 相似文献